Tuple types

Tuple types and relation types

Def: for any sets A and B, let A→B denote the set of functions that map from A to B.

A→B = { f | (f∈A⨯B) ∧ (dom(f)=A) ∧ (f is a function) }

Def: Let T be a given set of sets called a type system. Each element of T is called a type.

Let alpha = union(T).

Let A be a given set of attribute names. Let heading h∈(I→T) where I⊆A.

Define tuples(h) = { t | (t∈(I→alpha)) ∧ (∀a:(a∈I)→(t.a ∈ h.a) } and relations(h) = powerset(tuples(h))